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estimate the parameters of lognormal distribution by the some values of CDF

Asked by Alon Urlainis on 9 Feb 2019
Latest activity Commented on by Star Strider
on 9 Feb 2019
hello,
I want to find estimate the parameters of lognormal distribution by the some values of CDF
for example:
x= [0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00]
y= [0.000 0.000 0.005 0.022 0.051 0.091 0.138 0.188 0.240 0.291 0.341 0.389 0.434 0.476 0.515 0.552 0.586 0.617 0.646 0.672 0.696 0.719 0.739 0.758 0.776 0.792 0.806 0.820 0.832 0.844 0.854 0.864 0.873 0.881 0.889 0.896 0.903 0.909 0.915 0.920 0.925]
I want to estimate the mu and beta of the lognormal parameters
thanks

  5 Comments

Assuming this is the CDF, then it is close to complete, just missing part of the upper tail. The PDF would go down, but not the CDF.
I know. So give us the PDF since it's the PDF that has the log normal shape.
I know we can get it from the CDF but why not make it EASY for us to help you, not hard?

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3 Answers

Answer by Star Strider
on 9 Feb 2019
Edited by Star Strider
on 9 Feb 2019

Try this:
fcn = @(b,x) cdf('Lognormal',x,b(1),b(2));
x= [0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00];
y= [0.000 0.000 0.005 0.022 0.051 0.091 0.138 0.188 0.240 0.291 0.341 0.389 0.434 0.476 0.515 0.552 0.586 0.617 0.646 0.672 0.696 0.719 0.739 0.758 0.776 0.792 0.806 0.820 0.832 0.844 0.854 0.864 0.873 0.881 0.889 0.896 0.903 0.909 0.915 0.920 0.925];
[B,resnorm] = fminsearch(@(b) norm(y - fcn(b,x)), [1; 1]);
evf = fcn(B,x);
figure
plot(x, y, '.')
hold on
plot(x, evf, '-r')
hold off
grid
text(median(x), median(y)/2, sprintf('\\mu = %6.3f\n\\sigma = %6.3f', B))
EDIT — (9 Feb 2019 at 19:06)
estimate the parameters of lognormal distribution by the some values of CDF - 2019 02 09.png
EDIT — Added plot figure.

  1 Comment

@Alon Urlainis —
If my Answer helped you solve your problem, please Accept it!

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Answer by John D'Errico
on 9 Feb 2019

Looks like this does reasonably well to me.
fplot(@(x) logncdf(x,-.4,.75),[0,2])
hold on
plot(x,y,'.')
untitled.jpg

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Answer by Alon Urlainis on 9 Feb 2019

Thank you
Works great !!!

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